Dwork congruences via q-deformation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916723619266560 |
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| author | Kartik, Pavan Smirnov, Andrey |
| author_facet | Kartik, Pavan Smirnov, Andrey |
| contents | We consider a system of polynomials $T_{s}(z,q)\in\mathbb{Z}[z,q]$ which appear as truncations of the K-theoretic vertex function for the cotangent bundles over Grassmannians $T^{*}Gr(k,n)$. We prove that these polynomials satisfy a natural $q-$deformation of Dwork's congruences \[\frac{T_{s+1}(z,q)}{T_{s}(z^{p},q^{p})}\equiv\frac{T_{s}(z,q)}{T_{s-1}(z^{p},q^{p})}\text{ (mod } [p^{s}]_{q})\] In the limit $q\to 1$ we recover the main result of arXiv:2302.03092v3 |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04039 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dwork congruences via q-deformation Kartik, Pavan Smirnov, Andrey Number Theory Mathematical Physics Algebraic Geometry Representation Theory We consider a system of polynomials $T_{s}(z,q)\in\mathbb{Z}[z,q]$ which appear as truncations of the K-theoretic vertex function for the cotangent bundles over Grassmannians $T^{*}Gr(k,n)$. We prove that these polynomials satisfy a natural $q-$deformation of Dwork's congruences \[\frac{T_{s+1}(z,q)}{T_{s}(z^{p},q^{p})}\equiv\frac{T_{s}(z,q)}{T_{s-1}(z^{p},q^{p})}\text{ (mod } [p^{s}]_{q})\] In the limit $q\to 1$ we recover the main result of arXiv:2302.03092v3 |
| title | Dwork congruences via q-deformation |
| topic | Number Theory Mathematical Physics Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2505.04039 |